## In a class of 23 students, 9 play an instrument and 7 play a sport. There are 3 students who play an instrument and also play a sport. What

Question

In a class of 23 students, 9 play an instrument and 7 play a sport. There are 3 students who play an instrument and also play a sport. What is the probability that a student does not play an instrument given that they play a sport?

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7 days 2021-07-22T14:21:11+00:00 1 Answers 0 views 0

There are 23 students

— 9 students play neither sport

— therefore, 23 – 9  =  14 students play at least one of the two sports; some play both sports.

Inclusive or:  the probability will be:  14 / 23 that a student chosen at random will play at least one of the two sports.

Exclusive or: we need to first find how many students play both sports.

Since 14 persons play sports and since 7 play basketball and 12 play baseball, this requires 7 + 12 = 19 students.

Subtracting  19 – 14 = 5 give the number of students who play both sports.

If we eliminate these 5 persons as well as the 9 who play neither sport, we have to eliminate 5 + 9  =  14 persons.

This gives 23 – 14 = 9 persons who play only one of the two sports.

The probability will be:  9/23 play a sport, but only one sport.

Step-by-step explanation: